DESCRIPTION 



logic 



;: 



For this, the above principles obviously hold, and we may naturally denote it by -if 

 Then, if p denotes Protestantism, r Romanism, and f what is laN. . 



means either all Protestantism or all Romanism is false. In ihis v iy ii i< ph n that 

 all hypothetical propositions may be expressed. Moreover, if we suppose any term 

 as "man" (m) to be separated into its individual . M , M ", M , etc, then, 



M' if- M" if- M" i(- etc., 

 means "some man." This may very naturally be written 



-in' 



and this gives us an improved way of writing a particular proposition ; for 



<x' -< y 



seems a simpler way of writing " Some X is Y " than 



0*,J = . 



Converse, 



If we separate lover into its elementary relativ , take the reciprocal of each of 



these, that is, change it from 



A:B to B:A, 



and sum these reciprocals, we obtain the relative loved by. There is no such operation 

 as this in ordinary arithmetic, but if we suppose a science of di-rete quantity in 

 quaternion form (a science of equal intervals in space), the sum of the reap, lb of 

 the units of such a quaternion will be the conjugate-quaternion. For tins rea-,,, J 



express 



the conjugate term "what is related in the way that to - is -, to 

 by JL. The fundamental equations upon which the prope 



fth 



depend are 



(169.) 



JfC3£=1 . 



(170.) 



l£x<y z then *-<(-#>)* i 



or 



Ha?,y*)= \iz,-3£yx- 



We have, also, 



(171.) 

 (172.) 





j£n = ii-#, 



i „ ^v/ior Other equations will be found in 



where n denote the product in the reverse order. Utntr equa 



Mr. De Morgan's table, given above. 



